Quantitative Aptitude Notes: Chapter-wise Free PDF

SSC Quantitative Aptitude Notes: Complete Chapter-wise Study Material

Quantitative Aptitude is the section where SSC aspirants either build a winning score or lose precious marks. The questions are based on school-level mathematics, but they are asked under strict time pressure, so success depends on how well you know your formulas, shortcuts and calculation patterns. These SSC Quantitative Aptitude notes are written for SSC CGL, CHSL, MTS, GD Constable, CPO, Stenographer and other exams that test arithmetic and basic mathematics. Every chapter is explained in simple language with formulas, shortcut methods and solved examples.

Instead of reading one heavy textbook from cover to cover, you can pick a single chapter, learn the core idea, write the formulas in your revision sheet, and then test yourself with questions. This chapter-wise Maths notes for SSC approach suits students who are studying or working alongside preparation and can give only a few focused hours every day.

What You Get in These Quant Notes

• Chapter-wise explanation of every topic in the SSC mathematics syllabus
• Important formulas collected in one place for quick revision
• Shortcut tricks that save 20 to 30 seconds per question
• Solved examples in the style of real SSC question papers
• Common mistakes and how to avoid them
• Free online reading with downloadable PDFs for selected chapters

Why Quantitative Aptitude Decides Your Rank

In SSC CGL Tier 1 and CHSL Tier 1 the Quant section carries 25 questions out of 100, and in CGL Tier 2 the mathematics module has a much larger weightage. Because the questions are objective and the marking is sharp, a strong Quant score can lift your overall rank even if another section is average. Candidates who solve a calculation question in 40 seconds instead of 90 seconds also get extra time for reasoning and English, which improves the total score.

Complete Syllabus Covered in the Notes

• Number System: divisibility rules, HCF and LCM, remainders, unit digit, factors and prime numbers.
• Simplification and Approximation: BODMAS, surds and indices, square and cube roots, fraction comparison.
• Percentage, Ratio and Proportion, Average: the base chapters for every other arithmetic topic.
• Profit and Loss, Discount: cost price, selling price, marked price, successive discounts and dishonest dealings.
• Simple and Compound Interest: formulas, difference between SI and CI, instalments and population growth.
• Time and Work, Pipes and Cisterns: efficiency method, alternate-day work and negative work.
• Time, Speed and Distance, Trains, Boats and Streams: relative speed, average speed and upstream-downstream.
• Mixture and Alligation, Partnership, Ages: weighted average and ratio-based questions.
• Algebra: linear and quadratic equations, identities and maximum-minimum questions.
• Geometry: lines and angles, triangles and their centres, circles, tangents and quadrilaterals.
• Mensuration: area, perimeter, surface area and volume of 2D and 3D shapes.
• Trigonometry, Heights and Distances: ratios, identities, standard angles and application problems.
• Data Interpretation and Statistics: tables, bar graphs, pie charts, line graphs, mean, median and mode.

Quick Revision Notes for Important Quant Chapters

1. Number System

• A number is divisible by 2 if its last digit is even, by 3 or 9 if the sum of digits is divisible by 3 or 9, by 4 if the last two digits are divisible by 4, by 5 if it ends in 0 or 5, and by 8 if the last three digits are divisible by 8.
• A number is divisible by 11 if the difference between the sum of digits at odd places and even places is 0 or a multiple of 11.
• For two numbers, HCF x LCM = product of the numbers.
• Sum of the first n natural numbers = n(n + 1)/2, sum of the first n odd numbers = n squared, and sum of the first n even numbers = n(n + 1).
• If N = a^p x b^q x c^r (prime factors), the number of factors is (p + 1)(q + 1)(r + 1).

2. Percentage

• x% means x/100. Learn the fraction equivalents: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11% and 1/10 = 10%.
• Percentage change = (change / original value) x 100.
• If the price of an item rises by r%, the consumption must fall by r/(100 + r) x 100% to keep the expenditure the same.
• Successive changes of a% and b% give a net change of a + b + (ab/100)%.
• Population after n years at r% growth = P (1 + r/100) raised to n.

3. Profit, Loss and Discount

• Profit % = (SP - CP)/CP x 100 and Loss % = (CP - SP)/CP x 100.
• SP = CP x (100 + Profit%)/100 and CP = SP x 100/(100 + Profit%).
• Discount = Marked Price - Selling Price, and Discount % is always calculated on the marked price.
• Two successive discounts of a% and b% are equal to a single discount of a + b - (ab/100)%.
• If the selling price of two articles is the same and one is sold at x% profit and the other at x% loss, there is always an overall loss of x squared/100 %.

4. Simple and Compound Interest

• Simple Interest = (P x R x T)/100 and Amount = P + SI.
• Compound Amount = P (1 + R/100) raised to T, and CI = Amount - P.
• For 2 years, CI - SI = P x (R/100) squared. For 3 years, CI - SI = P x (R/100) squared x (3 + R/100).
• Effective rate for two successive rates of a% and b% = a + b + (ab/100)%.

5. Time and Work

• Efficiency = 1/days. Total work = efficiency x days.
• If A takes x days and B takes y days, together they take xy/(x + y) days.
• In the LCM method, take the LCM of the days as the total work units. This makes most questions a one-line calculation.
• M1 x D1 / W1 = M2 x D2 / W2 is the standard relation between men, days and work.

6. Time, Speed and Distance

• Speed = Distance / Time. To convert km/h to m/s multiply by 5/18, and for m/s to km/h multiply by 18/5.
• Relative speed is the sum of speeds when objects move in opposite directions and the difference when they move in the same direction.
• A train crossing a pole covers its own length; crossing a platform covers train length plus platform length.
• For boats, downstream speed = u + v and upstream speed = u - v, so the boat speed in still water is (D + U)/2 and the stream speed is (D - U)/2.
• If the distance is the same, average speed for two speeds x and y is 2xy/(x + y).

7. Algebra

• (a + b) squared = a squared + 2ab + b squared and (a - b) squared = a squared - 2ab + b squared.
• a squared - b squared = (a + b)(a - b).
• a cubed + b cubed = (a + b)(a squared - ab + b squared) and a cubed - b cubed = (a - b)(a squared + ab + b squared).
• If a + b + c = 0, then a cubed + b cubed + c cubed = 3abc.
• If x + 1/x = k, then x squared + 1/x squared = k squared - 2.

8. Geometry

• The sum of the angles of a triangle is 180 degrees, and an exterior angle equals the sum of the two opposite interior angles.
• The sum of interior angles of a polygon with n sides is (n - 2) x 180 degrees, and each exterior angle of a regular polygon is 360/n.
• The angle subtended by an arc at the centre is twice the angle at any point on the remaining circle, and a tangent is perpendicular to the radius at the point of contact.
• Opposite angles of a cyclic quadrilateral add up to 180 degrees.
• The centroid divides each median in the ratio 2:1. For the incentre I, angle BIC = 90 + A/2, for the circumcentre O, angle BOC = 2A, and for the orthocentre H, angle BHC = 180 - A.

9. Mensuration

• Circle: area = pi r squared and circumference = 2 pi r. Triangle: area = half x base x height; equilateral triangle: area = (root 3/4) a squared.
• Cube: volume = a cubed, total surface area = 6 a squared, diagonal = a root 3. Cuboid: volume = lbh, total surface area = 2(lb + bh + hl).
• Cylinder: curved surface area = 2 pi r h, volume = pi r squared h. Cone: volume = one third pi r squared h, slant height l = root of (r squared + h squared).
• Sphere: surface area = 4 pi r squared and volume = 4/3 pi r cubed. Hemisphere: curved surface area = 2 pi r squared and volume = 2/3 pi r cubed.

10. Trigonometry

• sin squared A + cos squared A = 1, 1 + tan squared A = sec squared A and 1 + cot squared A = cosec squared A.
• tan A = sin A / cos A and sin A x cosec A = 1.
• Standard values: sin 0, 30, 45, 60, 90 degrees = 0, 1/2, 1/root 2, root 3/2, 1. The values of cos are in the reverse order. tan 0, 30, 45, 60 = 0, 1/root 3, 1, root 3.

How to Study Quantitative Aptitude Notes Effectively

1. Learn the concept and formula of one chapter and write the formulas in a separate revision notebook.
2. Solve the examples yourself before looking at the solution, then compare your method with the shortcut method.
3. Practise 25 to 30 questions on that chapter in a fixed time and mark the ones you got wrong or guessed.
4. Revisit the marked questions after two days and again after a week. Spaced revision makes formulas stick.
5. After 6 to 8 chapters, start taking sectional mocks and previous year papers to build speed and accuracy.

A Simple 4-Week Study Plan

Week 1: Number System, Simplification, Percentage, Ratio, Average. Week 2: Profit and Loss, Interest, Time and Work, Speed and Distance. Week 3: Algebra, Geometry, Mensuration, Trigonometry. Week 4: Data Interpretation, revision of weak chapters and full-length practice. Adjust the pace to your schedule, but do not leave any chapter for the last month.

Common Mistakes to Avoid

• Memorising formulas without understanding when to apply them.
• Skipping calculation practice and relying on a calculator in daily life.
• Spending too long on one difficult question instead of moving on.
• Ignoring Geometry and Trigonometry because they look tough. They are scoring once the theorems are clear.
• Not revising. Without revision, a formula learned today is forgotten in a week.

Exam-Day Tips for the Quant Section

• Attempt the questions you know first and mark the long ones for later.
• Use approximation in options that are far apart instead of calculating the exact value.
• Check the units and the question statement once before marking the answer.
• Do not spend more than 90 seconds on a single question.

Practise With Previous Year Papers

Once you finish a few chapters, test yourself with our SSC previous year question papers and practice papers. Solving real exam questions shows which topics are repeated and how the difficulty changes from shift to shift. You can also read the other subject notes, such as Reasoning and English, to plan a balanced preparation for your SSC exam.

Frequently Asked Questions About SSC Notes

Where can I read SSC Quantitative Aptitude notes for free?

You can read every Quantitative Aptitude note on this page online without any signup or payment. Open a chapter from the list above, study the formulas and solved examples, and download the PDF wherever it is available so that you can revise offline.

Are these Quant notes enough for SSC CGL, CHSL and MTS?

The notes cover the complete arithmetic, algebra, geometry, mensuration and trigonometry syllabus that is asked in SSC CGL, CHSL, MTS, GD and CPO. For the best result, combine them with daily practice questions and previous year papers, because notes build the concept and practice builds speed.

How many hours a day should I study Quantitative Aptitude?

Two to three hours a day is a good target. Use the first hour to learn one chapter from the notes, and spend the remaining time on timed practice and on revising the mistakes you made earlier. A short daily routine works better than occasional long sessions.

Which Quant chapters should I study first?

Begin with Number System, Simplification, Percentage, Ratio and Proportion and Average because these are the base for almost everything else. Then move to Profit and Loss, Interest, Time and Work, Time Speed and Distance, and finally to Algebra, Geometry, Mensuration, Trigonometry and Data Interpretation.

Which are the most important chapters for SSC CGL Tier 1 and Tier 2?

Arithmetic chapters such as Percentage, Profit and Loss, Time and Work, Speed and Distance and Interest give steady marks. Geometry, Mensuration, Algebra and Trigonometry carry a heavy weight, especially in Tier 2. Data Interpretation is useful in both stages.

How can I improve my calculation speed?

Memorise tables up to 20, squares up to 30, cubes up to 15 and the common fraction-percentage equivalents. Practise approximation and mental calculation daily, and take timed sectional tests. Speed is a habit that grows with consistent practice.

What is the best way to remember Quant formulas?

Write each chapter formulas on one revision sheet, understand how the formula is derived, and apply it in at least ten questions. Revise the sheet after two days, one week and one month. Spaced revision is the most reliable way to keep formulas in long-term memory.

Should I learn shortcuts or concepts first?

Concepts first. A shortcut works only when you know why it works and when it does not. Once the concept is clear, learn the trick for that chapter, because it will save you valuable seconds in the exam.

Are the Quant notes useful for Hindi medium students?

Yes. The explanations use simple English, the formulas are universal, and solved examples are step by step, so Hindi medium students can follow them easily. You can also practise with the Hindi question papers available in our previous year papers section.

How many Quant questions come in SSC CGL Tier 1?

SSC CGL Tier 1 normally contains 25 Quantitative Aptitude questions out of 100. CHSL Tier 1 also has 25 questions. Tier 2 has a larger mathematics section. Always confirm the latest pattern in the official notification.

What should I do if I am weak in maths?

Do not panic. Start from the Class 6 to 10 basics, finish one chapter at a time, and solve easy questions first. Within four to six weeks of regular practice, most students see a clear improvement. Use these notes as your base and ask your doubts in the practice sessions.

How do I use previous year papers with these notes?

After you finish a chapter, search for its questions in the previous year papers and solve them. This shows how SSC frames the question, which formula is used, and how difficult the chapter can become in a real exam.